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A046704
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Additive primes: sum of digits is a prime.
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64
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2, 3, 5, 7, 11, 23, 29, 41, 43, 47, 61, 67, 83, 89, 101, 113, 131, 137, 139, 151, 157, 173, 179, 191, 193, 197, 199, 223, 227, 229, 241, 263, 269, 281, 283, 311, 313, 317, 331, 337, 353, 359, 373, 379, 397, 401, 409, 421, 443, 449, 461, 463, 467, 487, 557, 571, 577, 593
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OFFSET
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1,1
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COMMENTS
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Sum_{a(n) < x} 1/a(n) is asymptotic to (3/2)*log(log(log(x))) as x -> infinity; see Harman (2012). Thus the sequence is infinite. -Jonathan Sondow,Jun 07 2012
Harman 2012 also shows, under a conjecture about primes in short intervals, that there are 3/2 * x/(log x log log x) terms up to x. -Charles R Greathouse IV,Nov 17 2014
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LINKS
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EXAMPLE
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The digit sums of 11 and 13 are 1+1=2 and 1+3=4. Since 2 is prime and 4 is not, 11 is a member and 13 is not. -Jonathan Sondow,Jun 07 2012
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MAPLE
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select(n -> isprime(n) and isprime(convert(convert(n, base, 10), `+`)), [2, seq(2*i+1, i=1..1000)]); #Robert Israel,Nov 17 2014
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MATHEMATICA
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Select[Prime[Range[100000]], PrimeQ[Apply[Plus, IntegerDigits[ # ]]]&]
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PROG
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(PARI) isA046704(n)={local(s, m); s=0; m=n; while(m>0, s=s+m%10; m=floor(m/10)); isprime(n) & isprime(s)} \\Michael B. Porter,Oct 18 2009
(Magma) [ p: p in PrimesUpTo(600) | IsPrime(&+Intseq(p)) ]; //Bruno Berselli,Jul 08 2011
(Haskell)
a046704 n = a046704_list!! (n-1)
a046704_list = filter ((== 1). a010051. a007953) a000040_list
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CROSSREFS
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Indices of additive primes are inA075177.
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KEYWORD
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base,nonn
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AUTHOR
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STATUS
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approved
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